Modular conjugation (source code)

= Modular conjugation
{title2=$J$}

The antiunitary factor in the polar decomposition of the <Tomita operator>. In the finite-dimensional and tracial settings it satisfies $J^2=I$ and $JMJ=M'$. In a matrix-algebra standard representation by left multiplication, with positive invertible cyclic <vector> $D$, it acts by $J(X)=X^*$.